Patricia and Sandra have some apples.
Patricia says to Sandra, "If you give me 14 of your apples, I will have twice the number of apples left with you".
Sandra replies, "if you give me 14 of your apples I will have the same number of apples left with you".
Find the the number of apples with Patricia and Sandra separately.

1) The equivalent fraction is 27/8, so the correct option is A.

2) The value of the exponent in the right side must be y = 2, the correct option is C.

1) First we want to find an equivalent fraction to (2/3)^(-3)

Remember that a negative exponent means that we nee to take te inverse, we can write:

(2/3)^(-3) = (3/2)^3

Now we can just distribute the exponent along the numerator and denominator.

(3/2)^3 = (3^3)/(2^3) = 27/8

The correct option is A.

2) How to find the value of y?

Here we have the equation:

(3^3)^2/9^2 = 3^y

If we move the denominator to the right side, we can write:

(3^3)^2 = 9^2*3^y

Now, remember that:

9 = 3^2

Then we can write the right side as:

(9^2)*3^y = (3^2)^2*3^y = 3^(2*2)*3^y = 3^(4 + y)

Replacing that in the original equation we get:

(3^3)^2 = 3^(4 + y)

The exponent in the left side can be rewritten as:

(3^3)^2 = 3^(3*2) = 3^6

The the equation becomes:

3^6 = 3^(y + 4)

This is only true if:

6 = y + 4

6 - 4  =y

2 = y

The correct option is C.

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The values of a, b and c when comparing ⁷√(6³) with  [tex]a^\frac{b}{c}[/tex]  are 6, 21 and 2

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

⁷√(6³)

Applying the law of exponents gives:

= √[(6³)⁷]

= √[6²¹]

[tex]=6^\frac{21}{2}[/tex]

Given the form [tex]a^\frac{b}{c}[/tex], the values of a, b and c are 6, 21 and 2

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Answer:

the answer is number 4 okay

Answer:

it will roll on one of the sides after you roll it

Answer:

250b calories in b, bars 15c calories in c, carrots

Step-by-step explanation:

The simplified form of the ratio using the conversion 12 in = 1 ft as required in the task content is; Choice A; 8/1.

It follows from the task content that the simplified form of the ratio 8 ft / 12 in is to be determined.

Since the given ratio whose simplified form is to be determined is; 8 ft / 12 in.

However, recall that according to the conversion; 12 in = 1 ft.

On this note, 8 ft = 8 × 12 in.

Therefore, the equivalent ratio can be written as;

(8 × 12in) /12in.

The required simplified ratio is therefore; 8/1.

Ultimately, the correct answer choice is; Choice A; 8/1.

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Answer:

46.6 m/sec.

Step-by-step explanation:

Answer

500 tickets were sold

Step-by-step explanation:

Since 100 main floor tickets were sold, and each cost $7.50, we multiply it by 100 which equals $750, then since revenue was $3250, we do $3250 - $750 = $2500. Now that we got the extra tickets taken out of the way, time to find the rest. First, we add the prices of both tickets together, $7.50 + $5 = $12.50, then divide it by the remaining revenue, $2500 divided by $12.50 = 200 tickets, so 200 of each ticket were sold, + 100 main floor tickets. So now we do 300 main floor tickets + 200 balcony tickets, which is 500 tickets in total. Maybe you didn't read this but that's alright :)

Answer:

£56.16

Step-by-step explanation:

do 2 divided by 18.72 which is 9.36 then do 9.36×6 which is 56.16

Answer:

a number that is at least as large as 8.9

Step-by-step explanation:

the line under the greater than sign makes it equal to or greater than

As per the given equation, the distance between the two towns is 128 miles.

Equation:

Equation defined as the mathematical statement that is made up of two expressions connected by an equal sign.

Given,

A delivery truck drove 32 miles per hour. It took 4 hours to travel between two towns.

Here we need to find the distance between the two towns.

Here we know that, the equation

d=rt,

where

d is distance,

r is rate, and

t is fine.

Through the given question we have identified that the value of r (rate) is 32 miles per hour and the value of t (fine) is 4 hours.

So, the distance is,

d = 32 * 4

d = 128.

Therefore, the distance between the two towns is 128 mile.

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If FC bisects ∠ACD and ∠ACD is a straight angles, then proved that the ∠ACF is a right angle

The ∠ACD is a straight angles

We know the angles on a straight line add up to 180 degree

Therefore,

The measure of angle ACD = 180 degrees

Here it is given that the line FC bisects angle ACD

Therefore, The angle ACF is equal to Angel DCF

Angle ACF = Angel DCF

Angle ACF + Angle DCF = 180 degrees

Then,

Angle ACF = Angel DCF  = 90 degrees

Hence, if FC bisects ∠ACD and ∠ACD is a straight angles, then proved that the ∠ACF is a right angle

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Answer:

93.13

Step-by-step explanation:

   8 9 10                 This is to show the work

 99.00

-   5.87

------------

  93.13        

The order of cards on number line are in main body.

What is number line?

In elementary arithmetic, number line could be a image of a graduated line that is visual illustration of the important numbers. each purpose of range|variety} line is assumed to correspond to a true number, and each complex number to a degree.

Main body:

According to question we need to arrange numbers in ascending order ,

so the order will be as

-31/ 3 = -11.33

-10

-9/8 = -1.125

0

1/4 = 0.25

1

9/8 = 1.125

8

hence the order is as  -31/3< -10< -9/8 < 0< 1/4 < 1 < 9/8< 8

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Answer: area = 697.5 area

a. The terms are

b. The domain of the function is given as 1 ≤ x ≤ 4. The graph is a discrete graph

The term in the linear function m = 200 − 50v interpreted as

200 = money set aside for buying video games

50 = cost per video game

v = number pf video games

m = total amount spent on video games

The number refers to all the possible input values, this value as regard this context is when the money left for video game is finished.

the input value is v, the domain is solved as follows

200 - 50v = 0

50v = 200

v = 200/50

v = 4

The maximum number is 4 while the minimum is just above 0 or from 1 hence the domain is

1 ≤ x ≤ 4

the graph is attached

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If it reaches 250 bus stop shelters per month, then only the country can achieve their goal of 12000 bus stop shelters in 48 months.

Given,

The number of bus stop shelters a Country should built = 12,000

Time period for achieving the goal = 48 months

The average bus stop shelters the country can build in a month = more than 215

We have to explain that if they follow the above given format, will they achieve the goal in 48 months.

We can find it by using division operation;

Lets see;

Number of bus stop shelters they should build in one month = 12000/48 = 250

Here,

They are building more than 215 bus stop shelters per month.

If it reaches 250 bus stop shelters per month, then only the country can achieve their goal of 12000 bus stop shelters in 48 months.

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Answer:

False.

Step-by-step explanation:

E = mc² shows the relationship between mass and energy.

yeah bc the answer is 4 yrs

Answer:

3.5 years

Step-by-step explanation:

Answer:

Multiplication property

Step-by-step explanation:

Multiply each side by 8:

m=-2

m*8=8m

-2*8=-16

8m=-16

Number of winning tickets =7 and Number of losing tickets = 28. When there are 35 tickets in a bag and the ratio of winning tickets to losing tickets is 1:4

Given: Total tickets = 35

The ratio of winning tickets to losing tickets = 1:4

Number of winning tickets = [tex]\frac{1}{1+4} *35[/tex]

[tex]\frac{1}{5} *35=7[/tex]

Number of losing tickets = [tex]\frac{4}{1+4} *35[/tex]

[tex]\frac{4}{5} *35[/tex]

4×7=28

Hence, Number of winning tickets =7 and Number of losing tickets = 28.

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The approximate present value of this future income is $23,894.

What is interest?

Interest is a fee paid for borrowing money or other assets the amount borrowed is called the principal.

The interest is expressed as a percentage rate of the principal. for a given time interval.

What is percentage?

Percentages are essentially fractions where the denominator is 100.

What is Fraction?

A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator.

Formula of interest rate r is given by ;

Present value of future income [tex]= \frac{Income}{(1 + Interest\ rate)}[/tex]

Present value of future income [tex]= \frac{\$27000}{1+0.13}[/tex]

Present value of future income = $23,894

so, the option D is correct.

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The value of x is 33

What other external angles are there?

The alternate exterior angle theorem states that when two parallel lines cross, the exterior angles formed on either side of the transversal are equal. The distance between two intersecting lines or surfaces at or around their meeting point is referred to as the angle.

Since (2x - 30°) and (x+3)° are alternate exterior angles, they will be equivalent to one another.

(2x - 30)° = (x+3)°
Separate all similar phrases, then determine the value of x:
(2x - 30)° = (x+3)°
2x - x = 33 + 3
x = 33
Consequently, x will have the value of 33.

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The value of ∠C: 121°

What is Triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane.

Given this,

There is an ABC triangle.

m∠A = (x + 6)°

m∠B = (3x - 15)°

m∠C = (5x + 36)°

The size of C must be determined.

Having said that,

A triangle's total number of angles equals 180 degrees.

As a result, we can say,

∠(A) + ∠(B) + ∠(C) = 180

(x + 6)° + (3x - 15)° + (5x + 36)° = 180°

(x + 3x + 5x) + (6 - 15 + 36) = 180°

9x + 27 = 180°.

9x = 180 - 27

9x = 153 degrees

x = 153/9 degrees

17 = x.

Hence,

The ∠C  is expressed as

∠C = 5x + 36

= 5*17 + 36

= 85 + 36

∠C = 121.

Thus, ∠C = 121.

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All the answers to the given questions are mentioned below -

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

Given are six graphs as shown in the image.

The equation of graph [1] -

m = (- 2 - 4)/(2 - 0)

m = -6/2

m = -3

Equation : y = -3x + 4

The equation of graph [2] -

m = (0 + 1)/(2.5 - 0)

m = 1/2.5

m = 10/25

m = 2/5

Equation : y = 2x/5 - 1

The equation of graph [3] -

Equation : y = 4

The equation of graph [4] -

Equation : x = 2

[1] : 2x - y = - 7

y = 2x + 7

[2] : 5x + 3y = 12

3y = -5x + 12

y = -5x/2 + 4

[3] : x - y = 1

y = x - 1

[4] : x - 3y = - 15

3y = x + 15

y = x/3 + 5

[5] : 8x - 10y = 20

8x - 20 = 10y

y = 4x/5 - 2

[6] : 14x + 6y = 36

6y = -14x + 36

y = -7x/3 + 6

Therefore, all the answers to the given questions are mentioned above.

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[REFER TO IMAGE FOR QUESTION]

Answer:

The solution is -35/8

Step-by-step explanation:

[tex] \sf - 1 \frac{1}{4} \times 3 \frac{1}{2} \\ \\ = \sf - \frac{4 \times 1 + 1}{4} \times \frac{2 \times 3 + 1}{2} \\ \\ = \sf - \frac{4 + 1}{4} \times \frac{6 + 1}{2} \\ \\ = \sf - \frac{5}{4} \times \frac{7}{2} \\ \\ = \sf - \frac{5 \times 7}{4 \times 2} \\ \\ = \sf - \frac{35}{8} \\ \\ = \sf - 4 \frac{3}{8} [/tex]

Answer:

Step-by-step explanation:

so if you find the quadratic formula of 3 and multiply it by 82 you get 16. Then if you add 16 and 9 you get 25 this means that they sold 67 large pizzas. Your welcome

The expression that is similar to [tex]\frac{2^{3} . 2^{4} }{2^{12} }[/tex] is [tex]\frac{1}{2^{5} }[/tex]

Index (indices) in Maths is the power or exponent which is raised to a number or a variable. For example, in number [tex]2^{4}[/tex], 4 is the index of 2. The plural form of index is indices. In algebra, we come across constants and variables. The constant is a value which cannot be changed.

In the expression [tex]\frac{2^{3} . 2^{4} }{2^{12} }[/tex] all the indices have a common base 2

From numerator [tex]2^{3}[/tex] x [tex]2^{4}[/tex] = [tex]2^{3 + 4}[/tex]  which [tex]2^{7}[/tex]

so since the base at the numerator is same as that at the denominator we subtract their exponents

so that we have,

[tex]2^{7 - 12}[/tex] = [tex]2^{-5}[/tex]

which can further be written as  [tex]\frac{1}{2^{5} }[/tex]

In conclusion the simplified form of the expression is [tex]\frac{1}{2^{5} }[/tex]

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Work Shown:

h(x) = |x+10|

h(-17) = |-17+10|

h(-17) = |-7|

h(-17) = 7